Dynamically driven phase transformations in heterogeneous materials. I. Theory and microstructure considerations

Abstract

A theoretical model recently developed for heterogeneous materials undergoing dynamically driven thermodynamic phase transitions [F. L. Addessio et al. J. Appl. Phys. 97, 083509 (2005)] has been extended to allow for complex material microstructures. The model is applied to silicon carbide—titanium (SiC–Ti) unidirectional metal matrix composites where the aligned SiC fibers are filler and Ti is the matrix. Ti is known to undergo a low pressure and temperature solid-solid first-order phase transition. The microstructural analysis uses the generalized method of cells, which partitions a representative volume element into subcells containing the SiC fibers and the Ti matrix. The thermomechanical analysis has been reformulated from the previous work. In the reformulation it is found that thermodynamic quantities are naturally expressed as mass fraction averages over the two coexisting phases while the mechanical quantities are expressed naturally as volume averages. Consequently, the thermomechanical reformulation merges the mass averages typically found in thermodynamics with the volume averages used for mechanical properties of composites. Simulations have been pursued to study the complex interplay between loading, microstructure, and the thermomechanical response of the system as it undergoes the solid-solid Ti phase transformation. This is done for several different representative volume elements. For different orientations of loads relative to the fiber axes, the effect of local microstructure on the macroscopic stress-strain and thermodynamic response of the SiC–Ti composite is investigated.